I agree that you need to tell the doctor the truth. Even if you don't last that entire three weeks without drinking, he needs to know. Since alcohol IS a drug it could have effects when mixed with other medication.
Also, he/she might be able to provide resources to help reduce/quit drinking. I wonder if a referral to a therapist might even be helpful? You've had your life turned upside down, so you could probably use the support of a professionally-trained listening ear.
Look, you're doing great. If you're able to cut back then you're moving in the right direction. What you really need are coping skills and alcohol is not teaching them, even if it, admittedly, helps you to forget about your troubles temporarily.
Just don't get down on yourself if you don't make the entire three weeks dry. Quitting is often a two-steps-forward, one-step-back deal, and putting other coping skills in place is key for that continued improvement. So, use your doctor as a resource and make sure you get that blood pressure medicine refilled!
Best of luck!